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Mathematics
Problem
The polynomial
P
(
x
)
=
x
4
+
2
x
3
−
3
x
+
5
P(x)=x^{4}+2x^{3}-3x+5
P
(
x
)
=
x
4
+
2
x
3
−
3
x
+
5
is expressed in the form
(
x
2
+
a
x
+
b
)
(
x
2
+
1
)
+
(
c
x
+
d
)
(x^{2}+ax+b)(x^{2}+1)+(cx+d)
(
x
2
+
a
x
+
b
)
(
x
2
+
1
)
+
(
c
x
+
d
)
, where
a
,
b
,
c
,
a,\,b,\,c,
a
,
b
,
c
,
and
d
d
d
are integers. a. (i) Determine the values of
a
,
b
,
c
,
a,\,b,\,c,
a
,
b
,
c
,
and
d
d
d
. b. (ii) Write the complete identity obtained after substituting these values.
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